Symphony of double stars

Classical Mechanics Level 2

A binary star is a system of two stars in which both the stars revolve around a common point in space under their mutual gravitational attraction.

Which of the following is true for the stars?

Both the stars must have an equal time of revolution Both the stars must rotate in circular orbits Both the stars must have an equal orbital radius Both the stars must rotate at an equal speed

Rohit Gupta by Rohit Gupta , 34, India

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1 solution

Ahmed Aljayashi
Feb 14, 2019

  • The answer is the 4th option \text{4th option} : Closed celestial orbits are usually periodic , which means they repeat their motion from the start with constant time intervals , from that, it is necessary that both stars have an equal time of revolution .

  • 1sh option \text{1sh option} is canceled according to 1st law of Kepler .

  • 2nd option \text{2nd option} also is not valid because the ratio of orbital radius of each mass in a binary system equals their masses ratio.
  • 3rd option \text{3rd option} can't be true due to the possibility that their masses could be different so under equal force of gravity between them , each will have different centripetal acceleration, and hence different orbital speed .
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